text: /**
  BSD 3-Clause License
  
  This file is part of the Basalt project.
  https://gitlab.com/VladyslavUsenko/basalt.git
  
  Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
  
  * Redistributions of source code must retain the above copyright notice, this
    list of conditions and the following disclaimer.
  
  * Redistributions in binary form must reproduce the above copyright notice,
    this list of conditions and the following disclaimer in the documentation
    and/or other materials provided with the distribution.
  
  * Neither the name of the copyright holder nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
  FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  */
  
  #include <basalt/vi_estimator/marg_helper.h>
  #include <basalt/vi_estimator/sqrt_keypoint_vio.h>
  
  #include <basalt/optimization/accumulator.h>
  #include <basalt/utils/assert.h>
  #include <basalt/utils/system_utils.h>
  #include <basalt/vi_estimator/sc_ba_base.h>
  #include <basalt/utils/cast_utils.hpp>
  #include <basalt/utils/time_utils.hpp>
  
  #include <basalt/linearization/linearization_base.hpp>
  
  #include <fmt/format.h>
  
  #include <tbb/blocked_range.h>
  #include <tbb/parallel_for.h>
  #include <tbb/parallel_reduce.h>
  
  #include <chrono>
  
  namespace basalt {
  
  using namespace fmt::literals;
  
  template <class Scalar_>
  SqrtKeypointVioEstimator<Scalar_>::SqrtKeypointVioEstimator(
      const Eigen::Vector3d& g_, const basalt::Calibration<double>& calib_,
      const VioConfig& config_)
      : take_kf(true),
        frames_after_kf(0),
        g(g_.cast<Scalar>()),
        initialized(false),
        config(config_),
        lambda(config_.vio_lm_lambda_initial),
        min_lambda(config_.vio_lm_lambda_min),
        max_lambda(config_.vio_lm_lambda_max),
        lambda_vee(2) {
    obs_std_dev = Scalar(config.vio_obs_std_dev);
    huber_thresh = Scalar(config.vio_obs_huber_thresh);
    calib = calib_.cast<Scalar>();
  
    // Setup marginalization
    marg_data.is_sqrt = config.vio_sqrt_marg;
    marg_data.H.setZero(POSE_VEL_BIAS_SIZE, POSE_VEL_BIAS_SIZE);
    marg_data.b.setZero(POSE_VEL_BIAS_SIZE);
  
    // Version without prior
    nullspace_marg_data.is_sqrt = marg_data.is_sqrt;
    nullspace_marg_data.H.setZero(POSE_VEL_BIAS_SIZE, POSE_VEL_BIAS_SIZE);
    nullspace_marg_data.b.setZero(POSE_VEL_BIAS_SIZE);
  
    if (marg_data.is_sqrt) {
      // prior on position
      marg_data.H.diagonal().template head<3>().setConstant(
          std::sqrt(Scalar(config.vio_init_pose_weight)));
      // prior on yaw
      marg_data.H(5, 5) = std::sqrt(Scalar(config.vio_init_pose_weight));
  
      // small prior to avoid jumps in bias
      marg_data.H.diagonal().template segment<3>(9).array() =
          std::sqrt(Scalar(config.vio_init_ba_weight));
      marg_data.H.diagonal().template segment<3>(12).array() =
          std::sqrt(Scalar(config.vio_init_bg_weight));
    } else {
      // prior on position
      marg_data.H.diagonal().template head<3>().setConstant(
          Scalar(config.vio_init_pose_weight));
      // prior on yaw
      marg_data.H(5, 5) = Scalar(config.vio_init_pose_weight);
  
      // small prior to avoid jumps in bias
      marg_data.H.diagonal().template segment<3>(9).array() =
          Scalar(config.vio_init_ba_weight);
      marg_data.H.diagonal().template segment<3>(12).array() =
          Scalar(config.vio_init_bg_weight);
    }
  
    std::cout << "marg_H (sqrt:" << marg_data.is_sqrt << ")\n"
              << marg_data.H << std::endl;
  
    gyro_bias_sqrt_weight = calib.gyro_bias_std.array().inverse();
    accel_bias_sqrt_weight = calib.accel_bias_std.array().inverse();
  
    max_states = config.vio_max_states;
    max_kfs = config.vio_max_kfs;
  
    opt_started = false;
  
    vision_data_queue.set_capacity(10);
    imu_data_queue.set_capacity(300);
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::initialize(
      int64_t t_ns, const Sophus::SE3d& T_w_i, const Eigen::Vector3d& vel_w_i,
      const Eigen::Vector3d& bg, const Eigen::Vector3d& ba) {
    initialized = true;
    T_w_i_init = T_w_i.cast<Scalar>();
  
    last_state_t_ns = t_ns;
    imu_meas[t_ns] = IntegratedImuMeasurement<Scalar>(t_ns, bg.cast<Scalar>(),
                                                      ba.cast<Scalar>());
    frame_states[t_ns] = PoseVelBiasStateWithLin<Scalar>(
        t_ns, T_w_i_init, vel_w_i.cast<Scalar>(), bg.cast<Scalar>(),
        ba.cast<Scalar>(), true);
  
    marg_data.order.abs_order_map[t_ns] = std::make_pair(0, POSE_VEL_BIAS_SIZE);
    marg_data.order.total_size = POSE_VEL_BIAS_SIZE;
    marg_data.order.items = 1;
  
    nullspace_marg_data.order = marg_data.order;
  
    initialize(bg, ba);
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::initialize(const Eigen::Vector3d& bg_,
                                                     const Eigen::Vector3d& ba_) {
    auto proc_func = [&, bg = bg_.cast<Scalar>(), ba = ba_.cast<Scalar>()] {
      OpticalFlowResult::Ptr prev_frame, curr_frame;
      typename IntegratedImuMeasurement<Scalar>::Ptr meas;
  
      const Vec3 accel_cov =
          calib.dicrete_time_accel_noise_std().array().square();
      const Vec3 gyro_cov = calib.dicrete_time_gyro_noise_std().array().square();
  
      typename ImuData<Scalar>::Ptr data = popFromImuDataQueue();
      BASALT_ASSERT_MSG(data, "first IMU measurment is nullptr");
  
      data->accel = calib.calib_accel_bias.getCalibrated(data->accel);
      data->gyro = calib.calib_gyro_bias.getCalibrated(data->gyro);
  
      while (true) {
        vision_data_queue.pop(curr_frame);
  
        if (config.vio_enforce_realtime) {
          // drop current frame if another frame is already in the queue.
          while (!vision_data_queue.empty()) vision_data_queue.pop(curr_frame);
        }
  
        if (!curr_frame.get()) {
          break;
        }
  
        // Correct camera time offset
        // curr_frame->t_ns += calib.cam_time_offset_ns;
  
        if (!initialized) {
          while (data->t_ns < curr_frame->t_ns) {
            data = popFromImuDataQueue();
            if (!data) break;
            data->accel = calib.calib_accel_bias.getCalibrated(data->accel);
            data->gyro = calib.calib_gyro_bias.getCalibrated(data->gyro);
            // std::cout << "Skipping IMU data.." << std::endl;
          }
  
          Vec3 vel_w_i_init;
          vel_w_i_init.setZero();
  
          T_w_i_init.setQuaternion(Eigen::Quaternion<Scalar>::FromTwoVectors(
              data->accel, Vec3::UnitZ()));
  
          last_state_t_ns = curr_frame->t_ns;
          imu_meas[last_state_t_ns] =
              IntegratedImuMeasurement<Scalar>(last_state_t_ns, bg, ba);
          frame_states[last_state_t_ns] = PoseVelBiasStateWithLin<Scalar>(
              last_state_t_ns, T_w_i_init, vel_w_i_init, bg, ba, true);
  
          marg_data.order.abs_order_map[last_state_t_ns] =
              std::make_pair(0, POSE_VEL_BIAS_SIZE);
          marg_data.order.total_size = POSE_VEL_BIAS_SIZE;
          marg_data.order.items = 1;
  
          std::cout << "Setting up filter: t_ns " << last_state_t_ns << std::endl;
          std::cout << "T_w_i\n" << T_w_i_init.matrix() << std::endl;
          std::cout << "vel_w_i " << vel_w_i_init.transpose() << std::endl;
  
          if (config.vio_debug || config.vio_extended_logging) {
            logMargNullspace();
          }
  
          initialized = true;
        }
  
        if (prev_frame) {
          // preintegrate measurements
  
          auto last_state = frame_states.at(last_state_t_ns);
  
          meas.reset(new IntegratedImuMeasurement<Scalar>(
              prev_frame->t_ns, last_state.getState().bias_gyro,
              last_state.getState().bias_accel));
  
          while (data->t_ns <= prev_frame->t_ns) {
            data = popFromImuDataQueue();
            if (!data) break;
            data->accel = calib.calib_accel_bias.getCalibrated(data->accel);
            data->gyro = calib.calib_gyro_bias.getCalibrated(data->gyro);
          }
  
          while (data->t_ns <= curr_frame->t_ns) {
            meas->integrate(*data, accel_cov, gyro_cov);
            data = popFromImuDataQueue();
            if (!data) break;
            data->accel = calib.calib_accel_bias.getCalibrated(data->accel);
            data->gyro = calib.calib_gyro_bias.getCalibrated(data->gyro);
          }
  
          if (meas->get_start_t_ns() + meas->get_dt_ns() < curr_frame->t_ns) {
            if (!data.get()) break;
            int64_t tmp = data->t_ns;
            data->t_ns = curr_frame->t_ns;
            meas->integrate(*data, accel_cov, gyro_cov);
            data->t_ns = tmp;
          }
        }
  
        measure(curr_frame, meas);
        prev_frame = curr_frame;
      }
  
      if (out_vis_queue) out_vis_queue->push(nullptr);
      if (out_marg_queue) out_marg_queue->push(nullptr);
      if (out_state_queue) out_state_queue->push(nullptr);
  
      finished = true;
  
      std::cout << "Finished VIOFilter " << std::endl;
    };
  
    processing_thread.reset(new std::thread(proc_func));
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::addIMUToQueue(
      const ImuData<double>::Ptr& data) {
    imu_data_queue.emplace(data);
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::addVisionToQueue(
      const OpticalFlowResult::Ptr& data) {
    vision_data_queue.push(data);
  }
  
  template <class Scalar_>
  typename ImuData<Scalar_>::Ptr
  SqrtKeypointVioEstimator<Scalar_>::popFromImuDataQueue() {
    ImuData<double>::Ptr data;
    imu_data_queue.pop(data);
  
    if constexpr (std::is_same_v<Scalar, double>) {
      return data;
    } else {
      typename ImuData<Scalar>::Ptr data2;
      if (data) {
        data2.reset(new ImuData<Scalar>);
        *data2 = data->cast<Scalar>();
      }
      return data2;
    }
  }
  
  template <class Scalar_>
  bool SqrtKeypointVioEstimator<Scalar_>::measure(
      const OpticalFlowResult::Ptr& opt_flow_meas,
      const typename IntegratedImuMeasurement<Scalar>::Ptr& meas) {
    stats_sums_.add("frame_id", opt_flow_meas->t_ns).format("none");
    Timer t_total;
  
    if (meas.get()) {
      BASALT_ASSERT(frame_states[last_state_t_ns].getState().t_ns ==
                    meas->get_start_t_ns());
      BASALT_ASSERT(opt_flow_meas->t_ns ==
                    meas->get_dt_ns() + meas->get_start_t_ns());
  
      PoseVelBiasState<Scalar> next_state =
          frame_states.at(last_state_t_ns).getState();
  
      meas->predictState(frame_states.at(last_state_t_ns).getState(), g,
                         next_state);
  
      last_state_t_ns = opt_flow_meas->t_ns;
      next_state.t_ns = opt_flow_meas->t_ns;
  
      frame_states[last_state_t_ns] = PoseVelBiasStateWithLin<Scalar>(next_state);
  
      imu_meas[meas->get_start_t_ns()] = *meas;
    }
  
    // save results
    prev_opt_flow_res[opt_flow_meas->t_ns] = opt_flow_meas;
  
    // Make new residual for existing keypoints
    int connected0 = 0;
    std::map<int64_t, int> num_points_connected;
    std::unordered_set<int> unconnected_obs0;
    for (size_t i = 0; i < opt_flow_meas->observations.size(); i++) {
      TimeCamId tcid_target(opt_flow_meas->t_ns, i);
  
      for (const auto& kv_obs : opt_flow_meas->observations[i]) {
        int kpt_id = kv_obs.first;
  
        if (lmdb.landmarkExists(kpt_id)) {
          const TimeCamId& tcid_host = lmdb.getLandmark(kpt_id).host_kf_id;
  
          KeypointObservation<Scalar> kobs;
          kobs.kpt_id = kpt_id;
          kobs.pos = kv_obs.second.translation().cast<Scalar>();
  
          lmdb.addObservation(tcid_target, kobs);
          // obs[tcid_host][tcid_target].push_back(kobs);
  
          if (num_points_connected.count(tcid_host.frame_id) == 0) {
            num_points_connected[tcid_host.frame_id] = 0;
          }
          num_points_connected[tcid_host.frame_id]++;
  
          if (i == 0) connected0++;
        } else {
          if (i == 0) {
            unconnected_obs0.emplace(kpt_id);
          }
        }
      }
    }
  
    if (Scalar(connected0) / (connected0 + unconnected_obs0.size()) <
            Scalar(config.vio_new_kf_keypoints_thresh) &&
        frames_after_kf > config.vio_min_frames_after_kf)
      take_kf = true;
  
    if (config.vio_debug) {
      std::cout << "connected0 " << connected0 << " unconnected0 "
                << unconnected_obs0.size() << std::endl;
    }
  
    if (take_kf) {
      // Triangulate new points from one of the observations (with sufficient
      // baseline) and make keyframe for camera 0
      take_kf = false;
      frames_after_kf = 0;
      kf_ids.emplace(last_state_t_ns);
  
      TimeCamId tcidl(opt_flow_meas->t_ns, 0);
  
      int num_points_added = 0;
      for (int lm_id : unconnected_obs0) {
        // Find all observations
        std::map<TimeCamId, KeypointObservation<Scalar>> kp_obs;
  
        for (const auto& kv : prev_opt_flow_res) {
          for (size_t k = 0; k < kv.second->observations.size(); k++) {
            auto it = kv.second->observations[k].find(lm_id);
            if (it != kv.second->observations[k].end()) {
              TimeCamId tcido(kv.first, k);
  
              KeypointObservation<Scalar> kobs;
              kobs.kpt_id = lm_id;
              kobs.pos = it->second.translation().template cast<Scalar>();
  
              // obs[tcidl][tcido].push_back(kobs);
              kp_obs[tcido] = kobs;
            }
          }
        }
  
        // triangulate
        bool valid_kp = false;
        const Scalar min_triang_distance2 =
            Scalar(config.vio_min_triangulation_dist *
                   config.vio_min_triangulation_dist);
        for (const auto& kv_obs : kp_obs) {
          if (valid_kp) break;
          TimeCamId tcido = kv_obs.first;
  
          const Vec2 p0 = opt_flow_meas->observations.at(0)
                              .at(lm_id)
                              .translation()
                              .cast<Scalar>();
          const Vec2 p1 = prev_opt_flow_res[tcido.frame_id]
                              ->observations[tcido.cam_id]
                              .at(lm_id)
                              .translation()
                              .template cast<Scalar>();
  
          Vec4 p0_3d, p1_3d;
          bool valid1 = calib.intrinsics[0].unproject(p0, p0_3d);
          bool valid2 = calib.intrinsics[tcido.cam_id].unproject(p1, p1_3d);
          if (!valid1 || !valid2) continue;
  
          SE3 T_i0_i1 = getPoseStateWithLin(tcidl.frame_id).getPose().inverse() *
                        getPoseStateWithLin(tcido.frame_id).getPose();
          SE3 T_0_1 =
              calib.T_i_c[0].inverse() * T_i0_i1 * calib.T_i_c[tcido.cam_id];
  
          if (T_0_1.translation().squaredNorm() < min_triang_distance2) continue;
  
          Vec4 p0_triangulated = triangulate(p0_3d.template head<3>(),
                                             p1_3d.template head<3>(), T_0_1);
  
          if (p0_triangulated.array().isFinite().all() &&
              p0_triangulated[3] > 0 && p0_triangulated[3] < 3.0) {
            Keypoint<Scalar> kpt_pos;
            kpt_pos.host_kf_id = tcidl;
            kpt_pos.direction =
                StereographicParam<Scalar>::project(p0_triangulated);
            kpt_pos.inv_dist = p0_triangulated[3];
            lmdb.addLandmark(lm_id, kpt_pos);
  
            num_points_added++;
            valid_kp = true;
          }
        }
  
        if (valid_kp) {
          for (const auto& kv_obs : kp_obs) {
            lmdb.addObservation(kv_obs.first, kv_obs.second);
          }
        }
      }
  
      num_points_kf[opt_flow_meas->t_ns] = num_points_added;
    } else {
      frames_after_kf++;
    }
  
    std::unordered_set<KeypointId> lost_landmaks;
    if (config.vio_marg_lost_landmarks) {
      for (const auto& kv : lmdb.getLandmarks()) {
        bool connected = false;
        for (size_t i = 0; i < opt_flow_meas->observations.size(); i++) {
          if (opt_flow_meas->observations[i].count(kv.first) > 0)
            connected = true;
        }
        if (!connected) {
          lost_landmaks.emplace(kv.first);
        }
      }
    }
  
    optimize_and_marg(num_points_connected, lost_landmaks);
  
    if (out_state_queue) {
      PoseVelBiasStateWithLin p = frame_states.at(last_state_t_ns);
  
      typename PoseVelBiasState<double>::Ptr data(
          new PoseVelBiasState<double>(p.getState().template cast<double>()));
  
      out_state_queue->push(data);
    }
  
    if (out_vis_queue) {
      VioVisualizationData::Ptr data(new VioVisualizationData);
  
      data->t_ns = last_state_t_ns;
  
      for (const auto& kv : frame_states) {
        data->states.emplace_back(
            kv.second.getState().T_w_i.template cast<double>());
      }
  
      for (const auto& kv : frame_poses) {
        data->frames.emplace_back(kv.second.getPose().template cast<double>());
      }
  
      get_current_points(data->points, data->point_ids);
  
      data->projections.resize(opt_flow_meas->observations.size());
      computeProjections(data->projections, last_state_t_ns);
  
      data->opt_flow_res = prev_opt_flow_res[last_state_t_ns];
  
      out_vis_queue->push(data);
    }
  
    last_processed_t_ns = last_state_t_ns;
  
    stats_sums_.add("measure", t_total.elapsed()).format("ms");
  
    return true;
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::logMargNullspace() {
    nullspace_marg_data.order = marg_data.order;
    if (config.vio_debug) {
      std::cout << "======== Marg nullspace ==========" << std::endl;
      stats_sums_.add("marg_ns", checkMargNullspace());
      std::cout << "=================================" << std::endl;
    } else {
      stats_sums_.add("marg_ns", checkMargNullspace());
    }
    stats_sums_.add("marg_ev", checkMargEigenvalues());
  }
  
  template <class Scalar_>
  Eigen::VectorXd SqrtKeypointVioEstimator<Scalar_>::checkMargNullspace() const {
    return checkNullspace(nullspace_marg_data, frame_states, frame_poses,
                          config.vio_debug);
  }
  
  template <class Scalar_>
  Eigen::VectorXd SqrtKeypointVioEstimator<Scalar_>::checkMargEigenvalues()
      const {
    return checkEigenvalues(nullspace_marg_data, false);
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::marginalize(
      const std::map<int64_t, int>& num_points_connected,
      const std::unordered_set<KeypointId>& lost_landmaks) {
    if (!opt_started) return;
  
    Timer t_total;
  
    if (frame_poses.size() > max_kfs || frame_states.size() >= max_states) {
      // Marginalize
  
      const int states_to_remove = frame_states.size() - max_states + 1;
  
      auto it = frame_states.cbegin();
      for (int i = 0; i < states_to_remove; i++) it++;
      int64_t last_state_to_marg = it->first;
  
      AbsOrderMap aom;
  
      // remove all frame_poses that are not kfs
      std::set<int64_t> poses_to_marg;
      for (const auto& kv : frame_poses) {
        aom.abs_order_map[kv.first] = std::make_pair(aom.total_size, POSE_SIZE);
  
        if (kf_ids.count(kv.first) == 0) poses_to_marg.emplace(kv.first);
  
        // Check that we have the same order as marginalization
        BASALT_ASSERT(marg_data.order.abs_order_map.at(kv.first) ==
                      aom.abs_order_map.at(kv.first));
  
        aom.total_size += POSE_SIZE;
        aom.items++;
      }
  
      std::set<int64_t> states_to_marg_vel_bias;
      std::set<int64_t> states_to_marg_all;
      for (const auto& kv : frame_states) {
        if (kv.first > last_state_to_marg) break;
  
        if (kv.first != last_state_to_marg) {
          if (kf_ids.count(kv.first) > 0) {
            states_to_marg_vel_bias.emplace(kv.first);
          } else {
            states_to_marg_all.emplace(kv.first);
          }
        }
  
        aom.abs_order_map[kv.first] =
            std::make_pair(aom.total_size, POSE_VEL_BIAS_SIZE);
  
        // Check that we have the same order as marginalization
        if (aom.items < marg_data.order.abs_order_map.size())
          BASALT_ASSERT(marg_data.order.abs_order_map.at(kv.first) ==
                        aom.abs_order_map.at(kv.first));
  
        aom.total_size += POSE_VEL_BIAS_SIZE;
        aom.items++;
      }
  
      auto kf_ids_all = kf_ids;
      std::set<int64_t> kfs_to_marg;
      while (kf_ids.size() > max_kfs && !states_to_marg_vel_bias.empty()) {
        int64_t id_to_marg = -1;
  
        // starting from the oldest kf (and skipping the newest 2 kfs), try to
        // find a kf that has less than a small percentage of it's landmarks
        // tracked by the current frame
        if (kf_ids.size() > 2) {
          // Note: size > 2 check is to ensure prev(kf_ids.end(), 2) is valid
          auto end_minus_2 = std::prev(kf_ids.end(), 2);
  
          for (auto it = kf_ids.begin(); it != end_minus_2; ++it) {
            if (num_points_connected.count(*it) == 0 ||
                (num_points_connected.at(*it) /
                     static_cast<float>(num_points_kf.at(*it)) <
                 config.vio_kf_marg_feature_ratio)) {
              id_to_marg = *it;
              break;
            }
          }
        }
  
        // Note: This score function is taken from DSO, but it seems to mostly
        // marginalize the oldest keyframe. This may be due to the fact that
        // we don't have as long-lived landmarks, which may change if we ever
        // implement "rediscovering" of lost feature tracks by projecting
        // untracked landmarks into the localized frame.
        if (kf_ids.size() > 2 && id_to_marg < 0) {
          // Note: size > 2 check is to ensure prev(kf_ids.end(), 2) is valid
          auto end_minus_2 = std::prev(kf_ids.end(), 2);
  
          int64_t last_kf = *kf_ids.crbegin();
          Scalar min_score = std::numeric_limits<Scalar>::max();
          int64_t min_score_id = -1;
  
          for (auto it1 = kf_ids.begin(); it1 != end_minus_2; ++it1) {
            // small distance to other keyframes --> higher score
            Scalar denom = 0;
            for (auto it2 = kf_ids.begin(); it2 != end_minus_2; ++it2) {
              denom += 1 / ((frame_poses.at(*it1).getPose().translation() -
                             frame_poses.at(*it2).getPose().translation())
                                .norm() +
                            Scalar(1e-5));
            }
  
            // small distance to latest kf --> lower score
            Scalar score =
                std::sqrt(
                    (frame_poses.at(*it1).getPose().translation() -
                     frame_states.at(last_kf).getState().T_w_i.translation())
                        .norm()) *
                denom;
  
            if (score < min_score) {
              min_score_id = *it1;
              min_score = score;
            }
          }
  
          id_to_marg = min_score_id;
        }
  
        // if no frame was selected, the logic above is faulty
        BASALT_ASSERT(id_to_marg >= 0);
  
        kfs_to_marg.emplace(id_to_marg);
        poses_to_marg.emplace(id_to_marg);
  
        kf_ids.erase(id_to_marg);
      }
  
      //    std::cout << "marg order" << std::endl;
      //    aom.print_order();
  
      //    std::cout << "marg prior order" << std::endl;
      //    marg_order.print_order();
  
      if (config.vio_debug) {
        std::cout << "states_to_remove " << states_to_remove << std::endl;
        std::cout << "poses_to_marg.size() " << poses_to_marg.size() << std::endl;
        std::cout << "states_to_marg.size() " << states_to_marg_all.size()
                  << std::endl;
        std::cout << "state_to_marg_vel_bias.size() "
                  << states_to_marg_vel_bias.size() << std::endl;
        std::cout << "kfs_to_marg.size() " << kfs_to_marg.size() << std::endl;
      }
  
      Timer t_actual_marg;
  
      size_t asize = aom.total_size;
  
      bool is_lin_sqrt = isLinearizationSqrt(config.vio_linearization_type);
  
      MatX Q2Jp_or_H;
      VecX Q2r_or_b;
  
      {
        Timer t_linearize;
  
        typename LinearizationBase<Scalar, POSE_SIZE>::Options lqr_options;
        lqr_options.lb_options.huber_parameter = huber_thresh;
        lqr_options.lb_options.obs_std_dev = obs_std_dev;
        lqr_options.linearization_type = config.vio_linearization_type;
  
        ImuLinData<Scalar> ild = {
            g, gyro_bias_sqrt_weight, accel_bias_sqrt_weight, {}};
  
        for (const auto& kv : imu_meas) {
          int64_t start_t = kv.second.get_start_t_ns();
          int64_t end_t = kv.second.get_start_t_ns() + kv.second.get_dt_ns();
  
          if (aom.abs_order_map.count(start_t) == 0 ||
              aom.abs_order_map.count(end_t) == 0)
            continue;
  
          ild.imu_meas[kv.first] = &kv.second;
        }
  
        auto lqr = LinearizationBase<Scalar, POSE_SIZE>::create(
            this, aom, lqr_options, &marg_data, &ild, &kfs_to_marg,
            &lost_landmaks, last_state_to_marg);
  
        lqr->linearizeProblem();
        lqr->performQR();
  
        if (is_lin_sqrt && marg_data.is_sqrt) {
          lqr->get_dense_Q2Jp_Q2r(Q2Jp_or_H, Q2r_or_b);
        } else {
          lqr->get_dense_H_b(Q2Jp_or_H, Q2r_or_b);
        }
  
        stats_sums_.add("marg_linearize", t_linearize.elapsed()).format("ms");
      }
  
      //    KeypointVioEstimator::linearizeAbsIMU(
      //        aom, accum.getH(), accum.getB(), imu_error, bg_error, ba_error,
      //        frame_states, imu_meas, gyro_bias_weight, accel_bias_weight, g);
      //    linearizeMargPrior(marg_order, marg_sqrt_H, marg_sqrt_b, aom,
      //    accum.getH(),
      //                       accum.getB(), marg_prior_error);
  
      // Save marginalization prior
      if (out_marg_queue && !kfs_to_marg.empty()) {
        // int64_t kf_id = *kfs_to_marg.begin();
  
        {
          MargData::Ptr m(new MargData);
          m->aom = aom;
  
          if (is_lin_sqrt && marg_data.is_sqrt) {
            m->abs_H =
                (Q2Jp_or_H.transpose() * Q2Jp_or_H).template cast<double>();
            m->abs_b = (Q2Jp_or_H.transpose() * Q2r_or_b).template cast<double>();
          } else {
            m->abs_H = Q2Jp_or_H.template cast<double>();
  
            m->abs_b = Q2r_or_b.template cast<double>();
          }
  
          assign_cast_map_values(m->frame_poses, frame_poses);
          assign_cast_map_values(m->frame_states, frame_states);
          m->kfs_all = kf_ids_all;
          m->kfs_to_marg = kfs_to_marg;
          m->use_imu = true;
  
          for (int64_t t : m->kfs_all) {
            m->opt_flow_res.emplace_back(prev_opt_flow_res.at(t));
          }
  
          out_marg_queue->push(m);
        }
      }
  
      std::set<int> idx_to_keep, idx_to_marg;
      for (const auto& kv : aom.abs_order_map) {
        if (kv.second.second == POSE_SIZE) {
          int start_idx = kv.second.first;
          if (poses_to_marg.count(kv.first) == 0) {
            for (size_t i = 0; i < POSE_SIZE; i++)
              idx_to_keep.emplace(start_idx + i);
          } else {
            for (size_t i = 0; i < POSE_SIZE; i++)
              idx_to_marg.emplace(start_idx + i);
          }
        } else {
          BASALT_ASSERT(kv.second.second == POSE_VEL_BIAS_SIZE);
          // state
          int start_idx = kv.second.first;
          if (states_to_marg_all.count(kv.first) > 0) {
            for (size_t i = 0; i < POSE_VEL_BIAS_SIZE; i++)
              idx_to_marg.emplace(start_idx + i);
          } else if (states_to_marg_vel_bias.count(kv.first) > 0) {
            for (size_t i = 0; i < POSE_SIZE; i++)
              idx_to_keep.emplace(start_idx + i);
            for (size_t i = POSE_SIZE; i < POSE_VEL_BIAS_SIZE; i++)
              idx_to_marg.emplace(start_idx + i);
          } else {
            BASALT_ASSERT(kv.first == last_state_to_marg);
            for (size_t i = 0; i < POSE_VEL_BIAS_SIZE; i++)
              idx_to_keep.emplace(start_idx + i);
          }
        }
      }
  
      if (config.vio_debug) {
        std::cout << "keeping " << idx_to_keep.size() << " marg "
                  << idx_to_marg.size() << " total " << asize << std::endl;
        std::cout << "last_state_to_marg " << last_state_to_marg
                  << " frame_poses " << frame_poses.size() << " frame_states "
                  << frame_states.size() << std::endl;
      }
  
      if (config.vio_debug || config.vio_extended_logging) {
        MatX Q2Jp_or_H_nullspace;
        VecX Q2r_or_b_nullspace;
  
        typename LinearizationBase<Scalar, POSE_SIZE>::Options lqr_options;
        lqr_options.lb_options.huber_parameter = huber_thresh;
        lqr_options.lb_options.obs_std_dev = obs_std_dev;
        lqr_options.linearization_type = config.vio_linearization_type;
  
        nullspace_marg_data.order = marg_data.order;
  
        ImuLinData<Scalar> ild = {
            g, gyro_bias_sqrt_weight, accel_bias_sqrt_weight, {}};
  
        for (const auto& kv : imu_meas) {
          int64_t start_t = kv.second.get_start_t_ns();
          int64_t end_t = kv.second.get_start_t_ns() + kv.second.get_dt_ns();
  
          if (aom.abs_order_map.count(start_t) == 0 ||
              aom.abs_order_map.count(end_t) == 0)
            continue;
  
          ild.imu_meas[kv.first] = &kv.second;
        }
  
        auto lqr = LinearizationBase<Scalar, POSE_SIZE>::create(
            this, aom, lqr_options, &nullspace_marg_data, &ild, &kfs_to_marg,
            &lost_landmaks, last_state_to_marg);
  
        lqr->linearizeProblem();
        lqr->performQR();
  
        if (is_lin_sqrt && marg_data.is_sqrt) {
          lqr->get_dense_Q2Jp_Q2r(Q2Jp_or_H_nullspace, Q2r_or_b_nullspace);
        } else {
          lqr->get_dense_H_b(Q2Jp_or_H_nullspace, Q2r_or_b_nullspace);
        }
  
        MatX nullspace_sqrt_H_new;
        VecX nullspace_sqrt_b_new;
  
        if (is_lin_sqrt && marg_data.is_sqrt) {
          MargHelper<Scalar>::marginalizeHelperSqrtToSqrt(
              Q2Jp_or_H_nullspace, Q2r_or_b_nullspace, idx_to_keep, idx_to_marg,
              nullspace_sqrt_H_new, nullspace_sqrt_b_new);
        } else if (marg_data.is_sqrt) {
          MargHelper<Scalar>::marginalizeHelperSqToSqrt(
              Q2Jp_or_H_nullspace, Q2r_or_b_nullspace, idx_to_keep, idx_to_marg,
              nullspace_sqrt_H_new, nullspace_sqrt_b_new);
        } else {
          MargHelper<Scalar>::marginalizeHelperSqToSq(
              Q2Jp_or_H_nullspace, Q2r_or_b_nullspace, idx_to_keep, idx_to_marg,
              nullspace_sqrt_H_new, nullspace_sqrt_b_new);
        }
  
        nullspace_marg_data.H = nullspace_sqrt_H_new;
        nullspace_marg_data.b = nullspace_sqrt_b_new;
      }
  
      MatX marg_H_new;
      VecX marg_b_new;
  
      {
        Timer t;
        if (is_lin_sqrt && marg_data.is_sqrt) {
          MargHelper<Scalar>::marginalizeHelperSqrtToSqrt(
              Q2Jp_or_H, Q2r_or_b, idx_to_keep, idx_to_marg, marg_H_new,
              marg_b_new);
        } else if (marg_data.is_sqrt) {
          MargHelper<Scalar>::marginalizeHelperSqToSqrt(Q2Jp_or_H, Q2r_or_b,
                                                        idx_to_keep, idx_to_marg,
                                                        marg_H_new, marg_b_new);
        } else {
          MargHelper<Scalar>::marginalizeHelperSqToSq(Q2Jp_or_H, Q2r_or_b,
                                                      idx_to_keep, idx_to_marg,
                                                      marg_H_new, marg_b_new);
        }
  
        stats_sums_.add("marg_helper", t.elapsed()).format("ms");
      }
  
      {
        BASALT_ASSERT(frame_states.at(last_state_to_marg).isLinearized() ==
                      false);
        frame_states.at(last_state_to_marg).setLinTrue();
      }
  
      for (const int64_t id : states_to_marg_all) {
        frame_states.erase(id);
        imu_meas.erase(id);
        prev_opt_flow_res.erase(id);
      }
  
      for (const int64_t id : states_to_marg_vel_bias) {
        const PoseVelBiasStateWithLin<Scalar>& state = frame_states.at(id);
        PoseStateWithLin<Scalar> pose(state);
  
        frame_poses[id] = pose;
        frame_states.erase(id);
        imu_meas.erase(id);
      }
  
      for (const int64_t id : poses_to_marg) {
        frame_poses.erase(id);
        prev_opt_flow_res.erase(id);
      }
  
      lmdb.removeKeyframes(kfs_to_marg, poses_to_marg, states_to_marg_all);
  
      if (config.vio_marg_lost_landmarks) {
        for (const auto& lm_id : lost_landmaks) lmdb.removeLandmark(lm_id);
      }
  
      AbsOrderMap marg_order_new;
  
      for (const auto& kv : frame_poses) {
        marg_order_new.abs_order_map[kv.first] =
            std::make_pair(marg_order_new.total_size, POSE_SIZE);
  
        marg_order_new.total_size += POSE_SIZE;
        marg_order_new.items++;
      }
  
      {
        marg_order_new.abs_order_map[last_state_to_marg] =
            std::make_pair(marg_order_new.total_size, POSE_VEL_BIAS_SIZE);
        marg_order_new.total_size += POSE_VEL_BIAS_SIZE;
        marg_order_new.items++;
      }
  
      marg_data.H = marg_H_new;
      marg_data.b = marg_b_new;
      marg_data.order = marg_order_new;
  
      BASALT_ASSERT(size_t(marg_data.H.cols()) == marg_data.order.total_size);
  
      // Quadratic prior and "delta" of the current state to the original
      // linearization point give cost function
      //
      //    P(x) = 0.5 || J*(delta+x) + r ||^2.
      //
      // For marginalization this has been linearized at x=0 to give
      // linearization
      //
      //    P(x) = 0.5 || J*x + (J*delta + r) ||^2,
      //
      // with Jacobian J and residual J*delta + r.
      //
      // After marginalization, we recover the original form of the
      // prior. We are left with linearization (in sqrt form)
      //
      //    Pnew(x) = 0.5 || Jnew*x + res ||^2.
      //
      // To recover the original form with delta-independent r, we set
      //
      //    Pnew(x) = 0.5 || Jnew*(delta+x) + (res - Jnew*delta) ||^2,
      //
      // and thus rnew = (res - Jnew*delta).
  
      VecX delta;
      computeDelta(marg_data.order, delta);
      marg_data.b -= marg_data.H * delta;
  
      if (config.vio_debug || config.vio_extended_logging) {
        VecX delta;
        computeDelta(marg_data.order, delta);
        nullspace_marg_data.b -= nullspace_marg_data.H * delta;
      }
  
      stats_sums_.add("marg", t_actual_marg.elapsed()).format("ms");
  
      if (config.vio_debug) {
        std::cout << "marginalizaon done!!" << std::endl;
      }
  
      if (config.vio_debug || config.vio_extended_logging) {
        Timer t;
        logMargNullspace();
        stats_sums_.add("marg_log", t.elapsed()).format("ms");
      }
  
      //    std::cout << "new marg prior order" << std::endl;
      //    marg_order.print_order();
    }
  
    stats_sums_.add("marginalize", t_total.elapsed()).format("ms");
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::optimize() {
    if (config.vio_debug) {
      std::cout << "=================================" << std::endl;
    }
  
    if (opt_started || frame_states.size() > 4) {
      opt_started = true;
  
      // harcoded configs
      // bool scale_Jp = config.vio_scale_jacobian && is_qr_solver();
      // bool scale_Jl = config.vio_scale_jacobian && is_qr_solver();
  
      // timing
      ExecutionStats stats;
      Timer timer_total;
      Timer timer_iteration;
  
      // construct order of states in linear system --> sort by ascending
      // timestamp
      AbsOrderMap aom;
  
      for (const auto& kv : frame_poses) {
        aom.abs_order_map[kv.first] = std::make_pair(aom.total_size, POSE_SIZE);
  
        // Check that we have the same order as marginalization
        BASALT_ASSERT(marg_data.order.abs_order_map.at(kv.first) ==
                      aom.abs_order_map.at(kv.first));
  
        aom.total_size += POSE_SIZE;
        aom.items++;
      }
  
      for (const auto& kv : frame_states) {
        aom.abs_order_map[kv.first] =
            std::make_pair(aom.total_size, POSE_VEL_BIAS_SIZE);
  
        // Check that we have the same order as marginalization
        if (aom.items < marg_data.order.abs_order_map.size())
          BASALT_ASSERT(marg_data.order.abs_order_map.at(kv.first) ==
                        aom.abs_order_map.at(kv.first));
  
        aom.total_size += POSE_VEL_BIAS_SIZE;
        aom.items++;
      }
  
      // TODO: Check why we get better accuracy with old SC loop. Possible
      // culprits:
      // - different initial lambda (based on previous iteration)
      // - no landmark damping
      // - outlier removal after 4 iterations?
      lambda = Scalar(config.vio_lm_lambda_initial);
  
      // record stats
      stats.add("num_cams", this->frame_poses.size()).format("count");
      stats.add("num_lms", this->lmdb.numLandmarks()).format("count");
      stats.add("num_obs", this->lmdb.numObservations()).format("count");
  
      // setup landmark blocks
      typename LinearizationBase<Scalar, POSE_SIZE>::Options lqr_options;
      lqr_options.lb_options.huber_parameter = huber_thresh;
      lqr_options.lb_options.obs_std_dev = obs_std_dev;
      lqr_options.linearization_type = config.vio_linearization_type;
  
      std::unique_ptr<LinearizationBase<Scalar, POSE_SIZE>> lqr;
  
      ImuLinData<Scalar> ild = {
          g, gyro_bias_sqrt_weight, accel_bias_sqrt_weight, {}};
      for (const auto& kv : imu_meas) {
        ild.imu_meas[kv.first] = &kv.second;
      }
  
      {
        Timer t;
        lqr = LinearizationBase<Scalar, POSE_SIZE>::create(this, aom, lqr_options,
                                                           &marg_data, &ild);
        stats.add("allocateLMB", t.reset()).format("ms");
        lqr->log_problem_stats(stats);
      }
  
      bool terminated = false;
      bool converged = false;
      std::string message;
  
      int it = 0;
      int it_rejected = 0;
      for (; it <= config.vio_max_iterations && !terminated;) {
        if (it > 0) {
          timer_iteration.reset();
        }
  
        Scalar error_total = 0;
        VecX Jp_column_norm2;
  
        {
          // TODO: execution could be done staged
  
          Timer t;
  
          // linearize residuals
          bool numerically_valid;
          error_total = lqr->linearizeProblem(&numerically_valid);
          BASALT_ASSERT_STREAM(
              numerically_valid,
              "did not expect numerical failure during linearization");
          stats.add("linearizeProblem", t.reset()).format("ms");
  
          //        // compute pose jacobian norm squared for Jacobian scaling
          //        if (scale_Jp) {
          //          Jp_column_norm2 = lqr->getJp_diag2();
          //          stats.add("getJp_diag2", t.reset()).format("ms");
          //        }
  
          //        // scale landmark jacobians
          //        if (scale_Jl) {
          //          lqr->scaleJl_cols();
          //          stats.add("scaleJl_cols", t.reset()).format("ms");
          //        }
  
          // marginalize points in place
          lqr->performQR();
          stats.add("performQR", t.reset()).format("ms");
        }
  
        if (config.vio_debug) {
          std::cout << "[LINEARIZE] Error: " << error_total << " num points "
                    << std::endl;
          std::cout << "Iteration " << it << " " << error_total << std::endl;
        }
  
        // compute pose jacobian scaling
        //      VecX jacobian_scaling;
        //      if (scale_Jp) {
        //        // TODO: what about jacobian scaling for SC solver?
  
        //        // ceres uses 1.0 / (1.0 + sqrt(SquaredColumnNorm))
        //        // we use 1.0 / (eps + sqrt(SquaredColumnNorm))
        //        jacobian_scaling = (lqr_options.lb_options.jacobi_scaling_eps +
        //                            Jp_column_norm2.array().sqrt())
        //                               .inverse();
        //      }
        // if (config.vio_debug) {
        //   std::cout << "\t[INFO] Stage 1" << std::endl;
        //}
  
        // inner loop for backtracking in LM (still count as main iteration
        // though)
        for (int j = 0; it <= config.vio_max_iterations && !terminated; j++) {
          if (j > 0) {
            timer_iteration.reset();
            if (config.vio_debug) {
              std::cout << "Iteration " << it << ", backtracking" << std::endl;
            }
          }
  
          {
            // Timer t;
  
            // TODO: execution could be done staged
  
            //          // set (updated) damping for poses
            //          if (config.vio_lm_pose_damping_variant == 0) {
            //            lqr->setPoseDamping(lambda);
            //            stats.add("setPoseDamping", t.reset()).format("ms");
            //          }
  
            //          // scale landmark Jacobians only on the first inner
            //          iteration. if (scale_Jp && j == 0) {
            //            lqr->scaleJp_cols(jacobian_scaling);
            //            stats.add("scaleJp_cols", t.reset()).format("ms");
            //          }
  
            //          // set (updated) damping for landmarks
            //          if (config.vio_lm_landmark_damping_variant == 0) {
            //            lqr->setLandmarkDamping(lambda);
            //            stats.add("setLandmarkDamping", t.reset()).format("ms");
            //          }
          }
  
          // if (config.vio_debug) {
          //   std::cout << "\t[INFO] Stage 2 " << std::endl;
          // }
  
          VecX inc;
          {
            Timer t;
  
            // get dense reduced camera system
            MatX H;
            VecX b;
  
            lqr->get_dense_H_b(H, b);
  
            stats.add("get_dense_H_b", t.reset()).format("ms");
  
            if (config.vio_lm_pose_damping_variant == 1) {
              VecX Hdiag_lambda = (H.diagonal() * lambda).cwiseMax(min_lambda);
              H.diagonal() += Hdiag_lambda;
            }
  
            Eigen::LDLT<Eigen::Ref<MatX>> ldlt(H);
            inc = ldlt.solve(b);
            stats.add("solve", t.reset()).format("ms");
          }
  
          // backup state (then apply increment and check cost decrease)
          backup();
  
          // backsubstitute (with scaled pose increment)
          Scalar l_diff = 0;
          {
            // negate pose increment before point update
            inc = -inc;
  
            Timer t;
            l_diff = lqr->backSubstitute(inc);
            stats.add("backSubstitute", t.reset()).format("ms");
          }
  
          // undo jacobian scaling before applying increment to poses
          //        if (scale_Jp) {
          //          inc.array() *= jacobian_scaling.array();
          //        }
  
          // apply increment to poses
          for (auto& [frame_id, state] : frame_poses) {
            int idx = aom.abs_order_map.at(frame_id).first;
            state.applyInc(inc.template segment<POSE_SIZE>(idx));
          }
  
          for (auto& [frame_id, state] : frame_states) {
            int idx = aom.abs_order_map.at(frame_id).first;
            state.applyInc(inc.template segment<POSE_VEL_BIAS_SIZE>(idx));
          }
  
          // compute stepsize
          Scalar step_norminf = inc.array().abs().maxCoeff();
  
          // compute error update applying increment
          Scalar after_update_marg_prior_error = 0;
          Scalar after_update_vision_and_inertial_error = 0;
  
          {
            Timer t;
            computeError(after_update_vision_and_inertial_error);
            computeMargPriorError(marg_data, after_update_marg_prior_error);
  
            Scalar after_update_imu_error = 0, after_bg_error = 0,
                   after_ba_error = 0;
            ScBundleAdjustmentBase<Scalar>::computeImuError(
                aom, after_update_imu_error, after_bg_error, after_ba_error,
                frame_states, imu_meas, gyro_bias_sqrt_weight.array().square(),
                accel_bias_sqrt_weight.array().square(), g);
  
            after_update_vision_and_inertial_error +=
                after_update_imu_error + after_bg_error + after_ba_error;
  
            stats.add("computerError2", t.reset()).format("ms");
          }
  
          Scalar after_error_total = after_update_vision_and_inertial_error +
                                     after_update_marg_prior_error;
  
          // check cost decrease compared to quadratic model cost
          Scalar f_diff;
          bool step_is_valid = false;
          bool step_is_successful = false;
          Scalar relative_decrease = 0;
          {
            // compute actual cost decrease
            f_diff = error_total - after_error_total;
  
            relative_decrease = f_diff / l_diff;
  
            if (config.vio_debug) {
              std::cout << "\t[EVAL] error: {:.4e}, f_diff {:.4e} l_diff {:.4e} "
                           "step_quality {:.2e} step_size {:.2e}\n"_format(
                               after_error_total, f_diff, l_diff,
                               relative_decrease, step_norminf);
            }
  
            // TODO: consider to remove assert. For now we want to test if we even
            // run into the l_diff <= 0 case ever in practice
            // BASALT_ASSERT_STREAM(l_diff > 0, "l_diff " << l_diff);
  
            // l_diff <= 0 is a theoretical possibility if the model cost change
            // is tiny and becomes numerically negative (non-positive). It might
            // not occur since our linear systems are not that big (compared to
            // large scale BA for example) and we also abort optimization quite
            // early and usually don't have large damping (== tiny step size).
            step_is_valid = l_diff > 0;
            step_is_successful = step_is_valid && relative_decrease > 0;
          }
  
          double iteration_time = timer_iteration.elapsed();
          double cumulative_time = timer_total.elapsed();
  
          stats.add("iteration", iteration_time).format("ms");
          {
            basalt::MemoryInfo mi;
            if (get_memory_info(mi)) {
              stats.add("resident_memory", mi.resident_memory);
              stats.add("resident_memory_peak", mi.resident_memory_peak);
            }
          }
  
          if (step_is_successful) {
            BASALT_ASSERT(step_is_valid);
  
            if (config.vio_debug) {
              //          std::cout << "\t[ACCEPTED] lambda:" << lambda
              //                    << " Error: " << after_error_total <<
              //                    std::endl;
  
              std::cout << "\t[ACCEPTED] error: {:.4e}, lambda: {:.1e}, it_time: "
                           "{:.3f}s, total_time: {:.3f}s\n"
                           ""_format(after_error_total, lambda, iteration_time,
                                     cumulative_time);
            }
  
            lambda *= std::max<Scalar>(
                Scalar(1.0) / 3,
                1 - std::pow<Scalar>(2 * relative_decrease - 1, 3));
            lambda = std::max(min_lambda, lambda);
  
            constexpr Scalar initial_vee = Scalar(2.0);
            lambda_vee = initial_vee;
  
            it++;
  
            // check function and parameter tolerance
            if ((f_diff > 0 && f_diff < Scalar(1e-6)) ||
                step_norminf < Scalar(1e-4)) {
              converged = true;
              terminated = true;
            }
  
            // stop inner lm loop
            break;
          } else {
            std::string reason = step_is_valid ? "REJECTED" : "INVALID";
  
            if (config.vio_debug) {
              //          std::cout << "\t[REJECTED] lambda:" << lambda
              //                    << " Error: " << after_error_total <<
              //                    std::endl;
  
              std::cout << "\t[{}] error: {}, lambda: {:.1e}, it_time:"
                           "{:.3f}s, total_time: {:.3f}s\n"
                           ""_format(reason, after_error_total, lambda,
                                     iteration_time, cumulative_time);
            }
  
            lambda = lambda_vee * lambda;
            constexpr Scalar vee_factor = Scalar(2.0);
            lambda_vee *= vee_factor;
  
            //        lambda = std::max(min_lambda, lambda);
            //        lambda = std::min(max_lambda, lambda);
  
            restore();
            it++;
            it_rejected++;
  
            if (lambda > max_lambda) {
              terminated = true;
              message =
                  "Solver did not converge and reached maximum damping lambda";
            }
          }
        }
      }
  
      stats.add("optimize", timer_total.elapsed()).format("ms");
      stats.add("num_it", it).format("count");
      stats.add("num_it_rejected", it_rejected).format("count");
  
      // TODO: call filterOutliers at least once (also for CG version)
  
      stats_all_.merge_all(stats);
      stats_sums_.merge_sums(stats);
  
      if (config.vio_debug) {
        if (!converged) {
          if (terminated) {
            std::cout << "Solver terminated early after {} iterations: {}"_format(
                it, message);
          } else {
            std::cout
                << "Solver did not converge after maximum number of {} iterations"_format(
                       it);
          }
        }
  
        stats.print();
  
        std::cout << "=================================" << std::endl;
      }
    }
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::optimize_and_marg(
      const std::map<int64_t, int>& num_points_connected,
      const std::unordered_set<KeypointId>& lost_landmaks) {
    optimize();
    marginalize(num_points_connected, lost_landmaks);
  }
  
  template <class Scalar_>
  void SqrtKeypointVioEstimator<Scalar_>::debug_finalize() {
    std::cout << "=== stats all ===\n";
    stats_all_.print();
    std::cout << "=== stats sums ===\n";
    stats_sums_.print();
  
    // save files
    stats_all_.save_json("stats_all.json");
    stats_sums_.save_json("stats_sums.json");
  }
  
  // //////////////////////////////////////////////////////////////////
  // instatiate templates
  
  #ifdef BASALT_INSTANTIATIONS_DOUBLE
  template class SqrtKeypointVioEstimator<double>;
  #endif
  
  #ifdef BASALT_INSTANTIATIONS_FLOAT
  template class SqrtKeypointVioEstimator<float>;
  #endif
  
  }  // namespace basalt
  